Jackson is one of several players Chelsea are looking to move on before the end of the summer transfer window on September 1st.
The 25-year-old has been a long-term target for Aston Villa and Unai Emery, who remains a huge fan of Jackson following their time together at Villarreal.
According to The Athletic, the two club have now agreed a deal that would make Jackson the most expensive signing in Aston Villa’s history.
Villa will pay a fee of £47.5 million upfront for the Senegal international with add-ons taking the deal up to £65 million and personal terms in the process of being finalised.
Jackson’s move would mark the third time Chelsea and Villa have done business together this summer.
Morgan Rogers moved to Stamford Bridge in a club-record £117m transfer, while Alejandro Garnacho later joined Villa on a season-long loan, with a conditional obligation to buy.
The striker spent last season on loan at Bayern Munich, where he scored eight goals and provided two assists as an understudy to Harry Kane.
Current Aston Villa number nine Ollie Watkins is said to be pushing for a move to Saudi Arabian side Al Hilal.